A Communication-Efficient Stochastic Gradient Descent Algorithm for Distributed Nonconvex Optimization
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866909126028689408 |
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| author | Xie, Antai Yi, Xinlei Wang, Xiaofan Cao, Ming Ren, Xiaoqiang |
| author_facet | Xie, Antai Yi, Xinlei Wang, Xiaofan Cao, Ming Ren, Xiaoqiang |
| contents | This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We propose a distributed stochastic gradient descent (SGD) algorithm, suitable for a general class of compressors. We show that the proposed algorithm achieves the linear speedup convergence rate $\mathcal{O}(1/\sqrt{nT})$ for smooth nonconvex functions, where $T$ and $n$ are the number of iterations and agents, respectively. If the global cost function additionally satisfies the Polyak--Łojasiewicz condition, the proposed algorithm can linearly converge to a neighborhood of the global optimum, regardless of whether the stochastic gradient is unbiased or not. Numerical experiments are carried out to verify the efficiency of our algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Communication-Efficient Stochastic Gradient Descent Algorithm for Distributed Nonconvex Optimization Xie, Antai Yi, Xinlei Wang, Xiaofan Cao, Ming Ren, Xiaoqiang Optimization and Control This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We propose a distributed stochastic gradient descent (SGD) algorithm, suitable for a general class of compressors. We show that the proposed algorithm achieves the linear speedup convergence rate $\mathcal{O}(1/\sqrt{nT})$ for smooth nonconvex functions, where $T$ and $n$ are the number of iterations and agents, respectively. If the global cost function additionally satisfies the Polyak--Łojasiewicz condition, the proposed algorithm can linearly converge to a neighborhood of the global optimum, regardless of whether the stochastic gradient is unbiased or not. Numerical experiments are carried out to verify the efficiency of our algorithm. |
| title | A Communication-Efficient Stochastic Gradient Descent Algorithm for Distributed Nonconvex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.01322 |